On Some Properties of the Hofstadter–Mertens Function
Author
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-09-15
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
Many mathematicians have been interested in the study of recursive sequences.
Among them, a class of “chaotic” sequences are named “meta-Fibonacci sequences.” The main example of meta-Fibonacci sequence was introduced by Hofstadter, and it is called the Q-sequence.
Recently, Alkan–Fox–Aybar and the author studied the pattern induced by the connection between the Q-sequence and other known sequences.
Here, we continue this program by studying a “Mertens’ version” of the Hofstadter sequence, defined (for x>0) by x↦∑n≤xμnQn, where µ(n) is the Möbius function.
In particular, as we shall see, this function encodes many interesting properties which relate prime numbers to “meta-sequences”.
American Psychological Association (APA)
Trojovský, Pavel. 2020. On Some Properties of the Hofstadter–Mertens Function. Complexity،Vol. 2020, no. 2020, pp.1-6.
https://search.emarefa.net/detail/BIM-1139963
Modern Language Association (MLA)
Trojovský, Pavel. On Some Properties of the Hofstadter–Mertens Function. Complexity No. 2020 (2020), pp.1-6.
https://search.emarefa.net/detail/BIM-1139963
American Medical Association (AMA)
Trojovský, Pavel. On Some Properties of the Hofstadter–Mertens Function. Complexity. 2020. Vol. 2020, no. 2020, pp.1-6.
https://search.emarefa.net/detail/BIM-1139963
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1139963